Generalized staircases: Recurrence and symmetry

W. Patrick Hooper; Barak Weiss

doi:10.5802/aif.2730

Generalized staircases: Recurrence and symmetry

W. Patrick Hooper, Barak Weiss

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We study infinite translation surfaces which are ℤ-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Original language	American English
Pages (from-to)	1581-1600
Number of pages	20
Journal	Annales de l'Institut Fourier
Volume	62
Issue number	4
DOIs	https://doi.org/10.5802/aif.2730
State	Published - 12 Oct 2012

Keywords

Infinite translation surfaces
Lattices
Straightline flow
Veech groups

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Access to Document

10.5802/aif.2730

Cite this

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abstract = "We study infinite translation surfaces which are ℤ-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmith{\"u}sen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.",

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AB - We study infinite translation surfaces which are ℤ-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

KW - Infinite translation surfaces

KW - Lattices

KW - Straightline flow

KW - Veech groups

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M3 - Article

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ER -

Generalized staircases: Recurrence and symmetry

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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